Growth kinetics of ammonium oxalate monohydrate single crystals from aqueous solutions containing Co(II) and Ni(II) impurities

The growth kinetics of different faces of ammonium oxalate monohydrate (AO) single crystals from aqueous solutions containing different concentrations of Co(II) and Ni(II) ions at a constant temperature are described and discussed. It was found that: (1) at a given supersaturation σ, both Co(II) and Ni(II) ions lead to a decrease in the growth rates R of different faces of AO crystals, (2) the growth of a particular face of the crystals occurs above a critical supersaturation σ_d, but there is also another supersaturation barrier σ* when the rate abruptly increases with σ, and (3) the values of σ_d and σ* increase with increasing concentration c_i of the impurity. The experimental R(σ) data for different concentrations c_i of the impurities were analysed according to the model involving complex source of cooperating screw dislocations and concepts of instantaneous and time‐dependent impurity adsorption. Analysis of the data showed that: (1) adsorption of Co(II) and Ni(II) impurities occurs on the surface terrace of AO crystals, (2) there is a simple relationship between Langmuir constant K and the impurity concentration c_i* corresponding to maximum surface coverage, and (3) the ratio σ_d/σ* of the supersaturation barriers observed in the presence of both impurities increases with an increase in impurity concentration c_i, and may be explained from the standpoint of the mechanism of adsorption of impurity particles at kinks and ledges. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the origin of supersaturation barriers during the growth of single crystals from aqueous solutions containing impurities – a review

A generalised treatment of the appearance of supersaturation barriers σ_d, σ* and σ** during the growth of single crystals is outlined from the standpoint of well‐defined critical values of relative step velocities on a face. The final theoretical expressions are based on the premise that: (1) there are critical values of the relative step velocities associated with different average distances between adsorbed impurity particles during instantaneous, time‐dependent and time‐independent adsorption of the impurity on the growing surface, (2) the growth rate of a face is proporptional to velocity of steps on the growing face, and (3) Freundlich and Langmuir adsorption isotherms apply for different impurities. The theoretical expressions are then used to critically analyse the experimental data on supersaturation barriers observed during the growth of ammonium oxalate monohydrate and potassium dihydrogen phosphate single crystals from aqueous solutions containing different impurities. It was found that: (1) Langmuir adsorption isotherm is more practical for the analysis of the experimental data of the dependence of supersaturation barriers σ_d, σ* and σ** on the concentration c_i of an impurity, and (2) the ratios σ_d/σ* and σ*/σ** of successive supersaturation barriers for an impurity either increases or remains constant with an increase in impurity concentration c_i, and may be explained in terms of the mechanism of adsorption of impurity particles. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of Mn(II) ions on the growth of ammonium oxalate monohydrate crystals from aqueous solutions: I. Growth habit and surface morphology

The effect of concentration of Mn(II) ions on the growth habit and the surface micromorphology of different as‐grown faces of ammonium oxalate monohydrate (AO) single crystals grown from aqueous solutions was studied at a constant temperature of 30 °C and predefined supersaturations up to 20%. It was observed that the growth habit and the surface morphology of the crystals strongly depend on the supersaturation used for growth and the impurity concentration in the solution. The experimental results were analysed in terms of connected nets determined from different projections of the structure of AO crystals. Analysis of the observations revealed that: (1) the directions of connected nets corresponding to basic growth units composed of single (NH₄)₂C₂O₄ · H₂O molecules are in excellent agreement with the low‐index crystallographic directions of the orientations of growth layers, (2) all faces appearing in the growth morphology of AO crystals are F faces, and (3) the {001} face growing from pure aqueous solutions is essentially a kinetically rough face but the presence of Mn(II) impurity leads to their appearance in the morphology due to increase in the strength of bonds of the connected nets composing the surface graph.     

In situ study of growth and dissolution kinetics of ammonium oxalate monohydrate single crystals from aqueous solutions containing cationic impurities

The results of an in situ investigation of the effect of four different bi‐ and trivalent cations (Fe(III), Cu(II), Mn(II) and Cr(III)) on the displacement velocity of individual growth steps on the (110) face of ammonium oxalate monohydrate crystals as a function of supersaturation are described and discussed. It was observed that: (1) at a particular temperature of pure solutions and solutions containing impurities, the velocity v of movement of the [110] growth steps is always greater than that of the [111] steps, (2) fluctuations in the velocity of individual growth steps occur in all solutions containing similar concentrations of different impurities, (3) the value of kinetic coefficient β for growth steps decreases with an increase in the concentration c_i of Cu(II) impurity, but that for dissolution steps does not depend on c_i; moreover, the value of kinetic coefficient β for growth steps is higher than that of dissolution steps, and (4) in the presence of Mn(II) and Cr(III) impurities, the kinetic coefficient β for dissolution steps is several times greater than that for growth steps. The results are explained from the standpoint of Kubota‐Mullin model of adsorption of impurities at kinks in the steps and the stability of dominating complexes present in solutions. Analysis of the results revealed that: (1) the effectiveness of different impurities in inhibiting growth increases in the order: Fe(III), Cu(II), Mn(II), and Cr(III), and this behavior is directly connected with the stability and chemical constitution of dominating complexes in saturated solutions, (2) fluctuations in the velocity of growth steps is associated with the effectiveness of an impurity for adsorption; the stronger the adsorption of an impurity, the higher is the fluctuation in step velocity v, and (3) depending on the nature of the impurity, the kinetic coefficient for the dissolution steps can remain unchanged or can be higher than that of the growth steps. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth kinetics of zinc(tris)thiourea sulphate (ZTS) crystals

Growth kinetics of zinc (tris) thiourea sulphate (ZTS) crystals investigated as a function of supersaturation is reported in this communication. Crystal growth rates were investigated normal to the (100), (010) and (001) faces under growth conditions employed for bulk crystal growth. The growth rates normal to (010) and (100) were found to follow the continuous growth model (R_G = Cσ) with respect to the supersaturation whereas the growth rates normal to (001) was found to satisfy birth and spread (B+S) model (R_G = Aσ^5/6 exp(‐B/σ)). The growth rates observed normal to the studied face are in agreement with the growth mechanism predicted from the estimated α (Jackson) factor. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

In situ measurement of growth kinetics of {100} KDP crystal faces in the presence of polyphosphate impurities

The face growth rate and critical supersaturation of {100} face were in situ measured using the laser‐polarization‐interference technique in the presence of potassium pyrophosphate, trimetric sodium phosphate and sodium hexametaphosphate impurities. The polyphosphate impurities inhibit the growth rate of prismatic faces. The face growth rate as a function of supersaturation at different impurity concentrations, as well as critical supersaturation as a function of impurity concentrations, was found in good agreement with a two‐dimensional nucleation model in the pure system and Kubota and Mullin's model in the presence of impurities. The average distance L between active sites available for impurity adsorption as well as the edge free energy was calculated. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth kinetics and adsorption trapping of impurity during crystallization of NH<Subscript>4</Subscript>Cl in the NH<Subscript>4</Subscript>Cl-CuCl<Subscript>2</Subscript>-H<Subscript>2</Subscript>O-CONH<Subscript>3</Subscript> system

The growth of NH₄Cl crystals and their trapping of copper impurity in the NH₄Cl-CuCl₂-H₂O-CONH₃ quaternary system have been experimentally studied. The epitaxial adsorption of copper complexes on (100) faces leads to a sharp decrease in the growth rate in good correspondence with the Bliznakov-Chernov equation. The copper impurity enters the crystal composition in amounts up to 6.5 mol %. The impurity distribution coefficient nonlinearly changes with the copper concentration in the solution: it is much larger than unity at low concentrations and sharply decreases with an increase in supersaturation. Such behavior is indicative of the adsorption mechanism of copper trapping by NH₄Cl crystals. Single-crystal X-ray study shows that the impurity is incorporated in NH₄Cl crystals in the form of oriented intergrowths of different complex coppercontaining compounds. The concentration and variety of impurity phases increase with an increase in the copper content in the solution and decrease with an increase in supersaturation. Heterogeneous 2D isomorphous trapping of copper impurity by NH₄Cl crystals induces high (up to 60 MPa) internal stresses in them, as a result of which anomalous birefringence and splitting of crystals occur.     

Study of growth kinetics of ammonium oxalate monohydrate crystals from aqueous solutions

Experimental results of the dependence of linear growth rates of ammonium oxalate monohydrate [(NH₄)₂C₂O₄ · H₂O; AO] single crystals on solution supersaturation are presented. The AO crystals were grown by constant-temperature, constant-supersaturation method at 30 and 40 °C in the supersaturation range of 1–9%. It was observed that the supersaturation dependence of growth rates follows the parabolic growth law. Analysis of the supersaturation dependence of linear growth rates of AO crystals showed (1) that growth models involving surface diffusion and direct incorporation of growth units give kinetic parameters similar to those reported for other compounds grown from solutions, and (2) that the the BCF model of cooperating screw dislocations is also applicable. An inverse relationship between the estimated values of the length, L, of the line containing the dislocations and growth rate, R, and a direct relationship between L and interplanar distance, d_hkl, of the face {hkl} were found. Both these relationships are associated with the process of generation of screw dislocations in the growing layer.     

Effect of cationic impurities on solubility and crystal growth processes of ammonium oxalate monohydrate: Role of formation of metal‐oxalate complexes

The effect of different bi‐ and trivalent cationic impurities on the solubility of ammonium oxalate and the composition and distribution of chemical complexes formed in saturated ammonium oxalate aqueous solutions as a function of impurity concentration are investigated. The knowledge of the composition and stability of complexes formed in saturated aqueous solutions is then employed to explain the appearance of dead zones of supersaturation for growth and the difference in the effective segregation coefficient of the impurities. Analysis of the experimental results revealed that: (1) at a constant temperature, the dependence of concentration of complex species formed in saturated solutions on the concentration of different impurities can be described by an equation similar to that of the concentration dependence of density of solutions, (2) the dominant metal‐containing species present in saturated solutions are negatively‐charged, most stable oxalato complexes like Cu(C₂O₄)₂²⁻, Mn(C₂O₄)₃⁴⁻, Zn(C₂O₄)₃⁴⁻, Cr(C₂O₄)₃³⁻ and Fe(C₂O₄)₃³⁻, (3) in the investigated range of impurity concentration, the solubility of ammonium oxalates increases linearly with the concentration of all impurities and the increase is associated with the stability of dominant complexes, (4) appearance of dead supersaturation zones in the presence of impurities is associated with instantaneous adsorption of all growth sites by dominant oxalato complexes in relatively short adsorption time, and (5) the segregation coefficient of an impurity cation M of charge z + increases with a decrease in the solubility product constant K_sp for the hydrolysis products of reactions of the type: M^{z +} ↔ M₁^{(z −1)+} + H⁺ (where the cation M has z + charge, and H⁺ is hydrogen ion). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of nucleation kinetics and crystal defects of HMX

The nucleation kinetics of HMX (cyclotetramethylene tetranitramine, C₄H₈N₈O₈) in γ‐butyrolactone was studied in cooling process by induction time method. The laser scattering method was used to measure the solubility data and metastable region of HMX in γ‐butyrolactone. The induction time was measured over a range of supersaturation at different temperatures. Then, the nucleation mechanism of HMX in γ‐butyrolactone was investigated by analysis the relationships between induction time and supersaturation. The results indicated homogeneous nucleation dominated at high supersaturation of S >1.35, while the heterogeneous nucleation dominated at low supersaturation of S < 1.35. The values of interfacial tension at different final temperatures were calculated to indicate the ability of HMX to be crystallized. The growth mechanism of HMX was investigated by the data fitting applying different growth mechanism models and identified as two‐dimensional nucleation‐mediated (2D) growth. Finally, the effects of supersaturation and temperature on the crystal defects were analyzed based on the nucleation kinetics. When the temperature is below 303.15K, homogeneous nucleation dominated the nucleation process at higher supersaturation. Fine HMX crystals with more defects were produced. On the contrary, heterogeneous nucleation mechanism dominated at lower supersaturation. large regular HMX crystals with fewer defects were formed when the temperature is above 318.15K.     

Kinetic studies on the influence of temperature and growth rate history on crystal growth

Crystallization experiments of sucrose were performed in a batch crystallizer to study the effect of temperature and growth rate history on the crystal growth kinetics. In one of the growth methods adopted, the isothermal volumetric growth rate (R_V) is determined as a function of supersaturation (S) at 35, 40 and 45 ºC. In the other, crystals are allowed to grow at constant supersaturation by automatically controlling the solution temperature as the solute concentration decreased. Using the latter method R_V is calculated as the solution is cooled. The obtained results are interpreted using empirical, engineering and fundamental perspectives of crystal growth. Firstly, the overall activation energy (E_A) is determined from the empirical growth constants obtained in the isothermal method. The concept of falsified kinetics, widely used in chemical reaction engineering, is then extended to the crystal growth of sucrose in order to estimate the true activation energy (E_T) from the diffusion‐affected constant, E_A. The differences found in the isothermal and constant supersaturation methods are explained from the viewpoint of the spiral nucleation mechanism, taking into account different crystal surface properties caused by the growth rate history in each method. Finally, the crystal growth curve obtained in the batch crystallizer at 40 ºC is compared with the one obtained in a fluidized bed crystallizer at the same temperature. Apparently divergent results are explained by the effects of crystal size, hydrodynamic conditions and growth rate history on the crystallization kinetics of sucrose. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Curved-face growth of NaNO<Subscript>3</Subscript> crystals

Curved-face growth of NaNO₃ crystals under the action of the (NH₄)₂Mo₂O₇ impurity is studied experimentally and possible causes of face bending are analyzed. Selective impurity adsorption on the basal pinacoid results in growth of platelike crystals with spherically bent faces. Growth-rate measurements show that the impurity decelerates pinacoid-face growth by the Bliznakov kink-poisoning mechanism. Face bending can be explained by gradual deceleration of step growth by the impurities accumulated before step fronts. A model of step deceleration is suggested that is based on the assumption of slow impurity adsorption resulting in the instability of a step train. The model allows one to qualitatively interpret the experimental data.     

The Influence of Impurities on Crystallization Kinetics of Sodium Chloride

The influence of impurities on the crystallization kinetics of NaCl was investigated in a fluidized bed crystallizer. The growth and dissolution rates were related to the supersaturation and impurity concentrations. The effect of different impurities on the growth rate of NaCl crystals can be divided into thermodynamic effects where the impurities influence the solubility and kinetic effects where the impurities will suppress the growth rate compared to the pure NaCl. A mathematical model describing crystal growth rates from aqueous solution as a function of impurity concentration is presented. The model explains impurity concentration effects on the crystal growth rate in terms of an impurity effectiveness factor and a Langmuir adsorption isotherm for the impurity.     

Growth and Characterisation of Gel-grown Lead(II)Chloride and Lead(II)Bromide Single Crystals

Single crystals of pure and doped lead(II)chloride and lead(II)bromide were grown by gel technique employing a modified two-stage chemical reaction. Methods to minimise the predomination of needle morphology during the growth of these crystals have been investigated and the results are discussed. The grown crystals were characterised by optical transmission spectrum. Undoped and monovalent cation (K⁺, Na⁺, Cu⁺, Ag⁺ and Hg⁺) doped crystals of PbCl₂ and PbBr₂ were subjected to d.c. electrical conductivity studies. Using the log σT versus T⁻¹ plot, the activation energies for the migration of anion vacancies in lead(II)halides are calculated. They are found to be less for the doped crystals than those of undoped ones.     

Impurity adsorption mechanism of borax for a suspension growth condition: A comparison of models and experimental data

A fluidized bed crystallizer is employed to investigate the growth and dissolution rates of MgSO₄·7H₂O from aqueous solutions in the presence of borax as impurity at 25°C. By adding 0.5, 1, 2 and 5 wt % of impurity the pH value changes from 6.7 to 7.11, while the saturation temperature shifts to 24.8, 24.4, 24 and 23.1°C, respectively. The data on crystal growth rates from aqueous solutions as a function of impurity concentration are discussed from the standpoint of Cabrera and Vermileya, and Kubota and Mullin. The value of the impurity effect, αθ_eq, determined from analysis of the data on growth kinetics was found to be in good agreement with the value obtained from direct adsorption experiments. The estimated value of the average spacing between the adjacent adsorption active sites and the average distance between the neighbouring impurity‐adsorbed sites are also reported. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The role of hydration and complexing in the mechanism of impurity influence on crystal growth

The influence of impurities of chlorides and nitrates of divalent Ca²⁺ and Ba²⁺ cations on the kinetic growth of potassium dihydrophosphate KH₂PO₄ crystals at a saturation temperature of 323 K and relative supersaturation of 0.03 has been investigated experimentally. It is established that the impurity acts differently, depending on the face index, the impurity concentration, cation hydration, and the stability of the complexes formed in the solution by impurity salt ions. A model is proposed to explain the different influence of impurity ions on the growth of crystal faces. This influence is determined by the different hydration of cations and enhanced association of cations and anions of impurity salts in the surface layer with a lower dielectric constant.     

In situ AFM investigation of 2D nucleation on the (100) face of KDP

Surface morphology of the (100) face of potassium dihydrogen phosphate (KDP) crystals which were grown at different supersaturations at 25 °C was investigated by in situ atomic force microscopy (AFM). Various AFM images of 2D nucleation under different growth conditions were presented. It is found that the growth of KDP is controlled by polynuclear nucleation mechanism at the high supersaturation. With reduction of the supersaturation, the growth velocity of 2D nuclei becomes very slow and shows typical anisotropy. It is found that the process of coalescence of 2D nuclei does not lead to defect. The experiments show that the growth mechanism for KDP at 25 °C changes between step flow and 2D nucleation in the supersaturation range of 4.5‐5%. The triangular nuclei which are close to equilateral triangle are observed in the experiment at the supersaturation σ = 6% for the first time, showing typical anisotropic growth. Through observing the dissolution of 2D nuclei, the dissolving process can be regarded as the reverse process of growth. We also find that the microcrystals landing on the surface at σ = 9% would grow and coalesce with each other and there is no observable defect in the coalescence. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of crystal surface roughness on impurity adsorption

The effect of crystal surface roughness on impurity adsorption was investigated in a fluidized bed crystallizer and in a batch crystallizer. The crystallisation of sucrose in pure and impure systems was the study subject. Calcium chloride was utilized as impurity in this work. The results show that the impurity adsorption is growth rate dependent and is strongly influenced by the crystal surface properties. Crystals with high surface roughness have lower impurity adsorption. Based on experimental evidences, a new theoretical model is proposed to quantify the surface roughness influence on the impurity adsorption, allowing, by operating at the more adequate supersaturation, to control the impurity transfer into crystals. The used impurity does not have a significant influence on the growth rates at the studied temperatures. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Impurity effect of iron(III) on the growth of potassium sulfate crystal in aqueous solution

Growth rates of the {1 1 0} faces of a potassium sulfate crystal were measured in a flow cell in the presence of traces of impurity Fe(III) (up to 2 ppm) over the range of pH=2.5–6.0. The growth rate was significantly suppressed by the impurity. The effect became stronger as the impurity concentration was increased and at pH<5. It became weaker with increasing supersaturation. It also became weaker as the pH was increased and at pH>5 it finally disappeared completely. The concentration and supersaturation effects on the impurity action were reasonably explained with a model proposed by Kubota and Mullin [J. Crystal Growth, 152 (1995) 203]. The surface coverage of the active sites by Fe(III) is estimated to increase linearly on increasing its concentration in solution in the range examined by growth experiments. The impurity effectiveness factor is confirmed to increase inversely proportional to the supersaturation as predicted by the model. Apart from the discussion based on the model, the pH effect on the impurity action is qualitatively explained by assuming that the first hydrolysis product of aqua Fe(III) complex compound, [Fe(H₂O)₅(OH)]²⁺, is both growth suppression and adsorption active, but the second hydrolysis product, [Fe(H₂O)₄(OH)₂]⁺, is only adsorption active.     

Understanding supersaturation‐dependent crystal growth of L‐alanine in aqueous solution

The dependence of crystal growth rate of L‐alanine on solution supersaturation was investigated by combining experiments and molecular dynamics (MD) simulations. The experimental results show that lower supersaturated solution yields more elongated L‐alanine crystals along the c‐axis, i.e., the aspect ratio (c/b) of the crystal decreases with the increase of solution supersaturation, which is due to the higher supersaturation inducing a rise in the relative growth rate between the main side surface (the (120) surface) and the main end surface (the (011) surface). MD simulations on the two surfaces in contact with different supersaturated solutions revealed that the solute molecules tend to be more efficiently attached to the (011) surface than to the (120) surface at both supersaturations studied, as the interaction between the solute molecules and the L‐alanine molecules in the first layer of the (011) surface is stronger than that of the (120) surface. However, higher supersaturation leads to larger relative interaction energy between the (120) and (011) surfaces, suggesting an increase in the relative growth rate of the two surfaces (R₍₁₂₀₎/R₍₀₁₁₎) with supersaturation, which is in agreement with the experimental results.